The formula for the surface area of a sphere is:
`A = 4pir^2`
Note that the answer will be in square units eg cm2 or m2, as the answer is an area.
The diameter of a sphere is measured as 12cm. What, to 2 decimal places, is the surface area of the sphere?
| For a Sphere | Area | `= 4pir^2` |
| Substitute (`r=frac(1)(2) xx 12`) | `A` | `= pi(6)^2` |
| Divide both sides by 100 | `A` | `= 113.0973` |
Answer: 113.10 cm2
An experimental package is to be lowered into the sea to investigate global warming at the bottom of the ocean. Part of the experiment includes a hemisphere which is to be covered in a special coating. The hemisphere is solid, is of a constant thickness throughout and has no holes or apertures. The coating costs £4.50 per square centimetre.
The hemisphere has an external diameter of 40cm and has a constant thickness of 5mm. If the hemisphere has to be totally covered, what will the cost of the coating be?
Total Surface Area = Surface area outside + surface area inside + rim
Radius of outside = 40 ÷ 2 = 20cm
Radius of inside = 20 - 5 = 15cm
| Area Sphereoutside | Area | `= 4pir^2` |
| Substitute | `A` | `= 4pi(20)^2` |
| `= 5026.55` | ||
| Area Sphereinside | Area | `= 4pir^2` |
| Substitute | `= 4pi(15)^2` | |
| `= 2827.43` | ||
| Area Rimouter | Area | `= pir^2` |
| Substitute | `= pi(20)^2` | |
| `= 1256.64` | ||
| Area Riminner | Area | `= pir^2` |
| Substitute | `= pi(15)^2` | |
| `= 706.86` |
Total Surface Area
= 5026.55 + 2827.43 + (1256.64 - 706.86)
= 8403.76
Total Cost = 8403.76 x £4.50 = £37,816.92
Answer: £37816.92